Means for effecting improvements to mass spectrometers and mass filters

ABSTRACT

A mass or energy filter or spectrometer having a known electrode configuration such as quadrupole cylindrical, monopole cylindrical or hyperboloidal wherein the electrodes are energised by a periodic or quasi-periodic time varying electrical potential the waveform of which is significantly different from a sinusoid and incorporates a zeroth harmonic term in its Fourier series. It is preferred that the waveform should be either rectangular in character or trapezoidal in character and that means should be provided for varying the duty cycle of the waveform.

United States Patent [191 Hiller et al.

[ Nov. 18, 1975 MEANS FOR EFFECTING IMPROVEMENTS TO MASS SPECTROMETERS AND MASS FILTERS I [75] Inventors: John Barry Hiller, Thornleight;

John Alan Richards, Cranbrook; Richard Meredyth Huey, Sylvania, all of Australia [73] Assignee: Unisearch Limited, Kensington,

Australia 22 Filed: Jan.28, 1974 21 Appl. No.: 437,218

Related US. Application Data [63] Continuation-in-part of Ser. No. 238,564, March 27,

[52] US. Cl. 250/281; 250/292 [51] Int. Cl. H01j 39/34 [58] Field of Search 250/281, 282, 283, 292

[56] References Cited UNITED STATES PATENTS 3,413,463 11/1968 Brubaker ..250/292 SWITCHING NETWORK SOURCE OF WAVEFORM COMPONENTS -+-ADDER -1 OR l I l I 3,735,287 5/1973 Lowe 250/292 Primary Examiner-James W. Lawrence Assistant Examiner-C. E. Church Attorney, Agent, or FirmWenderoth, Lind & Ponack [57] ABSTRACT A mass or energy filter or spectrometer having a known electrode configuration such as quadrupole cylindrical, monopole cylindrical or hyperboloidal wherein the electrodes are energised by a periodic or quasi-periodic time varying electrical potential the waveform of which is significantly different from a sinusoid and incorporates a zeroth harmonic term in its Fourier series. It is preferred that the waveform should be either rectangular in character or trapezoidal in character and that means should be provided for varying the duty cycle of the waveform.

19 Claims, 12 Drawing Figures QUADRUPOLE MONOPOLE ELECTRODES SOURCE OF M.

us. Patent Nov. 18,1975 sheetlom 3,920,985

ri I l 2' I I I I l I l I I? l I I2 I2 I F l I 2; I l l msPLA I UNIT SINUSOIDAL I I7 OSCILLATOR SOURCE MASS FILTER P T I 0 PEAK F I655 I PEAK f PEAK U.S. Patent Nov. 18,1975 Sheet3of3 3,920,985

UNIT

l DISPLAY HT F|G.7a

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FIG.7c

This case is a continuation-in-part of application Ser. No. 238,564, filed on Mar. 27, 1972.

BACKGROUND OF THE INVENTION 1. Field of the Invention The invention relates to a mass or energy filter or spectrometer of the quadrupole type which is similar in operation to the mass filter described in the paper Paul W. and Raether M. Das elektrisch Massenfilter, Zeit Phys. Vol. 140, No. 3, May 1955, p. 262 the action of which was described by the Mathieu differential equa-, tion and which employed a focussing action on ions in flight throughan'electric field whichwas time-varying .in a manner described by the Mathieu equation, the

Mathieu equation being a particular form of the Hill equation. The operation of mass spectrometers according to the present invention is however based upon other formsof the Hill equation and employs analyzing electrode structures which include quadrupole and other configurations. j

2. Description of the Prior Art The mass spectrometers based upon the paper referred to above utilize a variety of analyzing electrodes configurations, e.g. quadrupole cylindrical, monopole cylindrical, or hyperboloidal. The present invention also employs these electrode configurations which are the bases for mass spectrometers of the kinds known respectively as quadrupole mass spectrometers, monopolemass spectrometers, and three-dimensional rotationally symmetric ion cages, all of which can be said to I function on the quadrupole principle, and which will be referred to compendiously in this specification as mass spectrometers of the quadrupole type. The structures of these various electrodes is well known in the art. The quadrupole cylindricalelectrode system consists, ideally, of four metallic parallel, symmetrical hyperbolic cylinders. In practice, this system is approximated by four parallel circular rods. The monopole cylindrical electrode system ideally consists of a single hyperbolic cylinder symmetrically located with respect to two electrically-continuousmetal planes intersecting at 90 and parallel to the axis of the cylinder. This system is, in practice, approximated by a single circular rod and one comer of a square tube. I-Iyperboloidal electrodes are metallic electrodes having the shape of hyperboloids of revolution. One particular form of hyperboloidal electrodes is referred to as a three dimensional rotationally symmetric ion cage. These various electrode configurations are used in mass spectrometers which may be, generally referred to as quadrupole type mass spectrometers. The authors referred to above and all subsequent workers have energised the analyzing electrodes of such mass spectrometers by an electric potential composed of a constant potential to which has been added a sinusoidally time-varying potential or by a plurality of sinusoidally time-varying potentials of discrete non-commensurate frequencies. It is to be noted that any references to electrodes in this specifiential equation. Such' mass spectrometers are described, inter alia, in US. Pat. Nos. 2,939,952 and 2,950,389 granted Jun. '7, 1960 and Aug. 23, 1960 to W. Paul et al., in US. Pat. No. 3,129,327 granted Apr. 14, 1964 to W. M. Brubaker and in US. Pat. No. 3,527,939 granted Sept. 8, 1970 to P. H. Dawson et al.

The present invention contemplates the use of a similar variety of electrode configurations the electrodes being energised by means arranged to generate the periodic time-varying electric potential which is defined below.

The analysis of ion flight through the electrode region is carried out by ascertaining and making use of appropriate solutions to the more general Hill differential equation rather than the Mathieu equation which is a particular case of the Hill equation.

SUMMARY OF THE INVENTION Instruments operating according to the present invention have improved characteristics as compared with existing instruments which give rise to the following advantages:

1. Improved insensitivity of operation to variations of operating parameters and variables in the electronic control units of the spectrometers and filters,v resulting in reduced complexity of electronic circuitry.

2. Instruments of conventional resolution and/or sensitivity can be constructed at a reduced cost.

3. Alternatively, instruments of higher resolutions and/or sensitivities can be constructed at the same cost.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a diagram illustrating the mechanical arrangements of the parts of a quadrupole mass filter or spectrometer,

FIG. 2 is a diagram showing the system used to ener-' gize the electrode in a conventional Paul-Mathieu type of mass spectrometer,

FIG. 3a illustrates the waveform used in a Paul-Mathieu type of mass spectrometer in which the potential applied to the electrodes is a combination of a dc potential and a sinusoidally varying potential,

FIG. 3b illustrates a rectangular waveform used according to the present invention,

FIG. 30 illustrates a trapezoidal waveform used according to the present invention.

FIG. 4 is a block diagram of means for energising the electrodes of a mass spectrometer with a time-varying potential according to the invention,

FIG. 5 is a block diagram of a further means for energising the electrodes of a mass spectrometer according to the invention,

FIG. 6 is a diagram illustrating the mechanical arrangement of the parts of a quadrupole mass filter or spectrometer in which auxiliary electrodes are arranged adjacent the main electrodes, and

FIGS. 7a to 7d are diagrams showing various alternative forms of electrical coupling between the main and auxiliary electrodes.

DESCRIPTION OF THE PREFERRED EMBODIMENT The broadest aspect of the present invention may be understood by considering the difference between the particular and relevant versions of the Hill equation, i.e. g(t) x =f(t) and the Mathieu equation i.e. i (a+b cos w t)x =f(t). In these equations, x represents the distance travelled by an ion from its source, and t 3 the time taken to travel that distance; a and b are constants. It is inherent in the specification that the timevarying function g(t) be periodic or very nearly so e.g. quasiperiodic or slowly swept periodic.

The Mathieu equation is a special case of the Hill equation where g(t) is allowed to be a constant plus a sinusoid and this would include the case where the constant was zero. The actual operation of mass spectrometers of the quadrupole type constructed and used to the present day'is described by this equation, following the disclosures in US. Pat. Nos. 2,939,952 and 2,950,389.. In these systems the constant portion of the function g(I) is related to a DC. or constant potential applied to the analysing electrodes of the mass spectrometers while the sinusoid is related to a high frequency sinusoidal potential generated separately from and applied to such electrodes together with said DC. potential. At the times of filing of U.S. Pat. Nos. 2,939,952 and 2,950,389 a sinusoidal potential would have been the most easily generated high frequency periodic waveform. An important limitation on the quality of measurements made with this mode of operation results from the need to maintain the ratio of the magnitude of the sinusoidal potential to the magnitude of the constant potential constant to tolerances which approach the limit even of present day electronic technology. This limitation also applies when the sinusoidal potential is replaced by any other periodic waveshape. The present invention does not include a mode of operation wherein a constant potential is applied to the analyzing electrodes of a mass spectrometer of the quadrupole type together with a high frequency periodic potential. Instead only one waveform is applied to the analyzing electrodes of such device being a waveform which contains its own constant component intrinsi- -cally by reason of the method by which it is generated.

An example of such a waveform and such a means for generation would be a rectangular waveform generated by an electronic switching circuit, where the repetition rate and duty cycle of the rectangular waveform can be controlled simply by controlling the operation of the switching circuit. Duty cycle is taken to means the time inverval over which the rectangular waveform is at its most positive potential divided by the period of the waveform. In the present therefore a DC. or constant potential is not generated separately from the highly frequency periodic potential and thus not applied together withthe high frequency potential, as it is for devices operated according to the disclosures in US. Pat. No. 2,939,952 and any ensuring specifications.

The waveforms to be used according to the present invention are required to be periodic and contain an intrinsic constant component which may be varied by changing a parameter of the waveform, such as the duty cycle in the example cited above. The actual shape of the waveform over one period is not important. This may be confirmed by noting that if the waveform is expanded in a Fourier series it may be shown that only the first three of four harmonics have any significant effect on the operation of mass spectrometers of the quadrupole type.

The time-varying function describing the electric potential applied to the electrodes of a mass spectrometer of the quadrupole type according to the present invention may be formed by a repetitive sequence of segments each one of which is composed of either one or a number of linearly-varying functions of time and/or one or a number of exponentially-varying functions of time where the exponents of each portion are either real functions of time or complex functions of time significantly different from purely imaginary functions of time.

The definition of the function g(t) according to the invention thus specifically excludes the case where g(t) is either a sinusoid or very nearly a sinusoid due to unavoidable deficiencies in the construction of electrical sinusoidal oscillators in the present state of the art where the harmonic content, although reasonably small, cannot be entirely reduced to zero.

The mathematical technique known as Fourier Analysis may be used with some particular examples to as sist in the explanation of the present invention. Fourier analysis states that any periodic waveform g(t) may be represented as a series of weighted sinusoidal terms with frequencies nf where f is the frequency corresponding to the period with which the waveform is repetitive and n is an integer which can take on the successive values from zero to infinity. For most practical purposes instead of proceeding to an infinite number of terms the Fourier series may be truncated at a term where n is a suitably chosen finite number taken not too large, and it is known that the error generated by performing this truncation will be not greater than the magnitude of the next succeeding term.

The frequencies of individual terms are thus commensurate i.e. can be expressed exactly by the ratio of two integers. In addition the phase angles to be attributed to each term will be coherent i.e. in some fixed relationship to each other due to the fact that the waveform is the output from a single generating source. In addition the weights i.e. coefficients attached to each term will bear to each other constant ratios which are A waveform which is exactly sinusoidal will have only one non-zero coefficient in its Fourier series expansion, i.e. the coefficient corresponding to the value n l.

Practically realizable sinusoidal oscillators generate harmonic terms i.e. frequencies with n 2, 3 etc. with small amplitudes and the output from such oscillators when provided by the conventional means of inductive and/or capacitive coupling will contain no D.C. term or zeroth harmonic term, i.e. the coefficient corresponding to the value n 0 will be zero.

On the other hand a periodic waveform which is rectangular or trapezoidal or substantially so in shape and which is arranged to possess equal and fixed or very nearly equal and fixed values of peak electric potential with respect to the earth or electric potential-reference node of its electric circuit will possess a Fourier series expansion with substantially nonzero coefficients for many terms including particularly n 0,1 and higher integers. Using the notation An to indicate the value of the coefficient in the term where the said integer is equal to n, each of the ratios An/Ao where n takes the values I, and higher integers will be fixed exactly and precisely by the shape of the waveform.

In the case of a waveform comprising a DC. component and a single sinusoidal component provided from separate sources the ratio Al/Ao will be determined by the characteristics including the stability of each of the two generating sources.

In the case of a waveform comprising a DC. component and a heirarchy of sinusoidal harmonics provided from a single source the ratio Al/Ao and also the ratios An/Ao where n 2 and higher integers will be determined solely by the shape of the waveform.

Such waveforms as are pertinent to-the present invention may be generated by the sequential summation in time of a convenientand practicably small number of successive segments or portions which are either lin-" early or-exponentially (with real or complex but notnumber of components whereas two hundred or one not restricted to, rectangular periodic or trapezoidal periodic (or quasiperiodic) or practically realizable approximations "tothese idealized waveforms are especially advantageous for the purposes of improving the performance and/or reducing the cost of mass spectrometers of the quadrupole type. These advantages are realizable compared to the equivalent mass spectrometers and mass filters whose electrodes are excited by constant electrical potentials or sinusoidal potentials generated at discrete non-commensurate frequencies or combinations of such constant and sinusoidal potentials.

In FIG. 1 is shown an electrode system of similar type to that used in a conventional Paul-Mathieu quadrupole mass spectrometer which is set up in a suitably evacuated chamber provided with an ion source 11 into which may be introduced small quantities .of the sample, compound or element under investigation. The quadrupole filter consists of four parallel metal electrodes 12, each approximating an electrically conducting cylindrical hyperboloid placed symmetrically about the device so that the necessary spatially-linear electrical field is closely realized. This filter is followed by an ion detector 13, which may be,.in the present state of the art, either a Faraday cup or an electron multiplier, but which in the future state of the art might alterna-- tively be an active electronic or quantum electronic device and which is employed, together with a suitable recording ordisplay unit, to register theabsolute or relative number of focussed ions which have been passed through the mass filter.

FIG. .shows the conventional arrangement for energising the electrodes of a mass filter or spectrometer as shown in FIG. 1. This consists of a sinusoidal oscillator source 14, a regulated D.C. source 15 and a means-to add these voltages 16 connected to the electrodes of a mass filter 17. FIG. 3a shows the waveform of the sinusoidal voltage and the waveform produced by combining them. i

FIG. 3b and FIG; 30 show respectively a rectangular and trapezoidal waveform which are two preferred waveforms for use in accordance with the present invention for energising the electrodes of a mass filter or spectrometer. The-dutycyclein the case of these two waveforms may be expressed as 7/1" or T-r/T.

In FIGS. .4 and 5 are shown, in simple block diagram form, arrangments for achieving the energisation of the electrodes of aI-Iill-equation type mass spectrometer of the quadrupole type by electrical potentials as described elsewhere in this document which may be generated'bya variety of means. The means indicated in the diagrams FIG. 4 and FIG. 5 exclude the necessity for a sinusoidal or quasi-sinusoidal electrical generator except for the likelihood that such a generator might be used as the initial reference within the periodic clock source. The various integers of these arrangements are named on thefigures. They are all conventional pieces of apparatus the nature and functioning of which is well known to those skilled in the art and they will not therefore be described in detail.

The means shown in FIG. 4 enables the generation of a nearly rectangular or nearly trapezoidal waveform whose duty cycle or mark-space ratio may be readily varied by manipulating the value of the adjustable time delay shown. It is a'further advantage of the invention that the added D.C. source as shown for example in FIG. 5, may be dispensed with and that if it is employed the ratio of the added D.C. potential to the alternating potential as used in the Mathieu-equation type mass spectrometers and filters does not have to be controlled very precisely as the major'means of mass selection. In the example shown in FIG. 4 it'will be evident that the DC. component may be controlled with great precision by the adjustable time delay as shown in the diagram FIG. 4. It is well known in the electronics art that timing of digital impulses may be controlled with great accuracy. On the other hand the control of the ratio of an alternating to a direct voltage as is required in the conventional Mathieru-equation type of mass spectrometer or mass filter cannot be achieved with such great accuracy nor with such inexpensive arrangements.

The use of a variable time delay, although convenient in some cases, is not essential to the generation of a waveform in which the amount of the DC. component of the time-varying waveform may be controlled so as to enable effective operation of a mass spectrometer or mass filter. For example in the arrangement shown in FIG. 5 the added D.C. source may be eliminated and the DC. component controlled entirely by the shape and amplitudes of the waveform components which may be switched at either fixed or variable time relative to the clock pulses provided by the periodic sources. Such means for switching at times either variable or fixed in relation to the pulses at clock frequency or at an integral multiple or submultiple of the clock frequency are well known in the electronics art.

It may also be advantageous in the present state of the art to incorporate auxiliary analyzing electrodes in order to influence ion trajectories particularly near the entry to the main electrodes. Such influence may be thought of either as prefocussing or as a pre-filtering in order to improve the sensitivity and/or resolution of the spectrometer. This artifice may also be employed profitably with the class of waveforms pertinent to the present invention. In FIG. 6 is shown an arrangement wherein the main electrodes 18 of a quadrupole mass spectrometer are energizedat points X X Y and Y by the waveforms described earlier in this specification and in which a DC. and higher frequency components are present in the Fourier series expansion of the waveis connected to a main electrode and the right hand side to an auxiliary analyzing electrode. In the case of the couplings shown in FIGS. 7a and 7b the ratio of the magnitude of the DC. component of the waveform applied to the auxiliary analyzing electrode to the magnitude of the other components is made zero. In the case of the coupling of FIG. 70 the ratio may be reduced and in that of FIG. 7d either increased or reduced depending on the circuit parameters.

A consideration of the effects of applying a rectangular R.F. waveform to the electrodes of a quadrupole mass spectrometer is set out in a paper by the present inventors entitled on the time varying potential in the quadrupole mass spectrometer published in the Proceeding of the Institution of Radio and Electronics Engineers Australia, August 1971 on page 321.

We claim:

1. In a mass spectrometer of the quadrupole type, the improvement comprising a single generating means for generating a single periodic time varying electrical output potential having both A.C. componentsand a DC. component, said potential having a segmented waveform formed by a repetitive sequence of discrete substantially linear segments each being composed of at least one substantially linearly varying function of time, and said generating means being operatively coupled to said mass spectrometer such that said potential may be applied to analyzing electrodes of said mass spectrometer.

2. The improved apparatus of claim I 'wherein said waveform is substantially rectangular and said generating means further comprises a means for varying the duty cycle of said waveform.

3. The improved apparatus of claim 1 wherein said waveform is substantially trapozoidal and said generating means further comprises means for varying the duty cycle of said waveform.

4. The improved mass spectrometer of claim 1 wherein said generating means further comprises means for varying the ratio of the amplitude of the DC. component to the AG components.

5. The improved mass spectrometer of claim 1 wherein said waveform is quadrilateral and said generating means further comprises means for varying the duty cycle of the waveform.

6. The system of claim 1' further comprising means for varying the amplitude of said waveform at a relatively slow rate whereby the mass-response of the mass spectrometer is scanned over a desired range.

7. The system of claim. 1 further comprising means for varying the repetition rate of said waveform at a relatively slow rate whereby the mass-response of the mass spectrometer is scanned over a desired range.

8. The improvement of claim 1 wherein said generating means comprises a source of substantially linear waveform components, a switch means operatively connecting said source to said analyzing electrodes for supplying a selected waveform to said analyzing electrodes of said mass spectrometer, and a source of clock pulses operatively connected to said switch for activating said switch for varying the waveform which is applied to said analyzing electrodes.

9. A mass spectrometer of the quadrupole type, comprising:

a single means for generating a single periodic time varying electrical output potential having both A.C. components and a DC. component, said potential having a segmented waveform formed by a repetitive sequence of discrete segments each being composed of at least one substantially linearly varying function of time and said means being operatively coupled to said mass spectrometer such that said potential may be applied to analyzing electrodes of said mass spectrometer;

auxiliary analyzing electrodes positioned between an ion source and said analyzing electrodes; and

means for energizing said auxiliary analyzing electrodes, connected thereto.

10. The system of claim 9 further comprising means for varying the amplitude of said waveform at a relatively slow rate whereby the mass-response of the mass spectrometer is scanned over a desired range.

11. The system of claim 9 further comprising means for varying the repitition rate of said waveform at a relatively slow rate whereby the mass-response of the mass spectrometer is scanned over a desired range.

12. In a mass spectrometer of the quadrupole type, the improvement comprising means for generating a single time varying electrical output potential having a segmented waveform,

said potential being formed by a repetitive sequence of discrete segments each being composed of at least one substantially exponentially varying function of time expressed as:

a b (c M) t where a, b, c, d are real constants, cl 0 and said means being operatively coupled to said mass spectrometer such that said potential may be applied to analyzing electrodes of said mass spectrometer.

13. The improved apparatus of claim 12 wherein said waveform is substantially rectangular and said generating means further comprises means for varying the duty cycle of said waveform.

14. The improved apparatus of claim 12 wherein said waveform is substantially trapezoidal and said generating means further comprises a means for varying the duty cycle of said waveform. I

15. The improved mass spectrometer of claim 12 wherein said generating means further comprises means for varying the ratio of the amplitude of the constant a to the other terms.

16. The improved mass spectrometer of claim 12 wherein said waveform is a quadrilateral and said generating means further comprises means for varying the duty cycle of the waveform.

17. The system of claim 12 further comprising auxiliary analyzing electrodes operatively coupled to said means for generating a single time varying electrical output potential.

18. The system of claim 12 further comprising means for varying the amplitude of said waveform at a relatively slow rate whereby the mass-response of the mass spectrometer is scanned over a desired range.

19. The system of claim 12 further comprising means for varying the repetition rate of said waveform at a relatively slow rate whereby the mass-response of the mass spectrometer is scanned over a desired range. 

1. In a mass spectrometer of the quadrupole type, the improvement comprising a single generating means for generating a single periodic time varying electrical output potential having both A.C. components and a D.C. component, said potential having a segmented waveform formed by a repetitive sequence of discrete substantially linear segments each being composed of at least one substantially linearly varying function of time, and said generating means being operatively coupled to said mass spectrometer such that said potential may Be applied to analyzing electrodes of said mass spectrometer.
 2. The improved apparatus of claim 1 wherein said waveform is substantially rectangular and said generating means further comprises a means for varying the duty cycle of said waveform.
 3. The improved apparatus of claim 1 wherein said waveform is substantially trapozoidal and said generating means further comprises means for varying the duty cycle of said waveform.
 4. The improved mass spectrometer of claim 1 wherein said generating means further comprises means for varying the ratio of the amplitude of the D.C. component to the A.C. components.
 5. The improved mass spectrometer of claim 1 wherein said waveform is quadrilateral and said generating means further comprises means for varying the duty cycle of the waveform.
 6. The system of claim 1 further comprising means for varying the amplitude of said waveform at a relatively slow rate whereby the mass-response of the mass spectrometer is scanned over a desired range.
 7. The system of claim 1 further comprising means for varying the repetition rate of said waveform at a relatively slow rate whereby the mass-response of the mass spectrometer is scanned over a desired range.
 8. The improvement of claim 1 wherein said generating means comprises a source of substantially linear waveform components, a switch means operatively connecting said source to said analyzing electrodes for supplying a selected waveform to said analyzing electrodes of said mass spectrometer, and a source of clock pulses operatively connected to said switch for activating said switch for varying the waveform which is applied to said analyzing electrodes.
 9. A mass spectrometer of the quadrupole type, comprising: a single means for generating a single periodic time varying electrical output potential having both A.C. components and a D.C. component, said potential having a segmented waveform formed by a repetitive sequence of discrete segments each being composed of at least one substantially linearly varying function of time and said means being operatively coupled to said mass spectrometer such that said potential may be applied to analyzing electrodes of said mass spectrometer; auxiliary analyzing electrodes positioned between an ion source and said analyzing electrodes; and means for energizing said auxiliary analyzing electrodes, connected thereto.
 10. The system of claim 9 further comprising means for varying the amplitude of said waveform at a relatively slow rate whereby the mass-response of the mass spectrometer is scanned over a desired range.
 11. The system of claim 9 further comprising means for varying the repitition rate of said waveform at a relatively slow rate whereby the mass-response of the mass spectrometer is scanned over a desired range.
 12. In a mass spectrometer of the quadrupole type, the improvement comprising means for generating a single time varying electrical output potential having a segmented waveform, said potential being formed by a repetitive sequence of discrete segments each being composed of at least one substantially exponentially varying function of time expressed as: a + be (c jd) t - Infinity <t< Infinity where a, b, c, d are real constants, c >0 and said means being operatively coupled to said mass spectrometer such that said potential may be applied to analyzing electrodes of said mass spectrometer.
 13. The improved apparatus of claim 12 wherein said waveform is substantially rectangular and said generating means further comprises means for varying the duty cycle of said waveform.
 14. The improved apparatus of claim 12 wherein said waveform is substantially trapezoidal and said generating means further comprises a means for varying the duty cycle of said waveform.
 15. The improved mass spectrometer of claim 12 wherein said generating means further comprises means for varying the ratio of the amplitude of the constant a to thE other terms.
 16. The improved mass spectrometer of claim 12 wherein said waveform is a quadrilateral and said generating means further comprises means for varying the duty cycle of the waveform.
 17. The system of claim 12 further comprising auxiliary analyzing electrodes operatively coupled to said means for generating a single time varying electrical output potential.
 18. The system of claim 12 further comprising means for varying the amplitude of said waveform at a relatively slow rate whereby the mass-response of the mass spectrometer is scanned over a desired range.
 19. The system of claim 12 further comprising means for varying the repetition rate of said waveform at a relatively slow rate whereby the mass-response of the mass spectrometer is scanned over a desired range. 